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This number would be 0.0005 per day and person. Let's do the computation.
Let's look at the given data. What do we know about each infected person?
As every other person, each infected person that meets 25 persons a day.
All this susceptible persons can be infected, so the question is how many
susceptible persons are among these 25?
We can compute that by ratio.
If there are 1,000 people in total, then the ratio of the number
of susceptible persons divided by the total of 1,000 persons
times these 25 persons that would be susceptible.
Imagine, everybody was susceptible then we would compute 1,000 persons times 25.
All 25 would be susceptible. If every second person was susceptible, 500 divided by 1,000
results in one half times 25, every second person would be susceptible.
So this is the number of contacts between a single infected person and susceptible persons per day
and each of these contacts will lead to infection with a probability of 2%.
So now, we can compute how many persons are infected by the single infected person per day
versus the number of contact of susceptible persons per day and multiply with probability.
This will be the number of new infections per day.
We can cancel the persons, these three numbers combine to 0.0005 per day
and per infected person, and that's precisely the expression we are needing in the SIR equations.
Constant times the number of susceptible persons times the number of infected persons.
But keep in mind that we are dealing with average values here,
25 persons per day give or take a probability of 2%, things can occur more often or less often.